2019
Том 71
№ 9

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Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. I

Bonafede S.

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Abstract

This paper is concerned with the existence and uniqueness of variational solutions of the strongly nonlinear equation $$ - \sum\limits_1^m {_i \frac{\partial }{{\partial x_i }}\left( {\sum\limits_1^m {_j a_{i,j} (x, u(x))\frac{{\partial u(x)}}{{\partial x_j }}} } \right) + g(x, u(x)) = f(x)} $$ with the coefficients a i,j (x, s) satisfying an eHipticity degenerate condition and hypotheses weaker than the continuity with respect to the variable s. Furthermore, we establish a condition on f under which the solution is bounded in a bounded open subset Ω of Rm.

English version (Springer): Ukrainian Mathematical Journal 48 (1996), no. 7, pp 977-987.

Citation Example: Bonafede S. Strongly nonlinear degenerate elliptic equations with discontinuous coefficients. I // Ukr. Mat. Zh. - 1996. - 48, № 7. - pp. 867-875.

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